CN111934730B - Symbol-level NOMA (non-synchronous access point) non-synchronous receiving method based on cross-slot message transfer algorithm - Google Patents
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Abstract
The invention discloses a symbol-level NOMA (non-asynchronous multiple access) receiving method based on a cross-slot message transfer algorithm, relates to a symbol-level non-orthogonal multiple access asynchronous multi-user detection method based on a factor graph, and belongs to the field of communication. The implementation method of the invention comprises the following steps: the time dimension is introduced into a traditional two-dimensional factor graph to form a time slot spanning message transmission method based on a three-dimensional factor graph model, the code elements of each user are estimated by spanning time slots on each frequency resource used for transmission by using the message transmission method, multi-user detection of an asynchronous LDS system is realized, the problem that the traditional symbol-level NOMA system can only carry out synchronous transmission is solved, symbol-level NOMA asynchronous reception is realized, the data transmission efficiency is improved, the capability range of the LDS system is expanded, and the availability of the LDS in massive Internet of things communication is enhanced.
Description
Technical Field
The invention relates to a Non-Orthogonal Multiple Access (NOMA) asynchronous multi-user detection method based on a factor graph, in particular to a multi-user detection method of an uplink asynchronous LDS system of an asynchronous transmission, an uplink Low-Density Signature (LDS) system and a message transfer algorithm, and belongs to the field of communication.
Technical Field
In recent years, the wireless communication system connection equipment has been increased explosively, and the problem of scarcity of frequency resources is gradually highlighted. In order to alleviate the problem of scarce wireless resources, the academic world proposes a non-orthogonal multiple access technology, which improves the utilization rate of frequency spectrum and gradually becomes a promising technology.
The non-orthogonal multiple access technology is a technology capable of performing multi-user transmission on the same wireless resource, and is an enabling technology with important potential for realizing throughput improvement under the scene of massive internet of things communication. In a massive internet of things communication scene, how to realize accurate receiving of massive data under the condition of asynchronous transmission is one of research focuses of multiple access technologies. Current non-orthogonal multiple access techniques can be divided into two categories: 1) bit-level NOMA, which is realized by using techniques such as bit expansion, bit interleaving and the like, and can adopt serial interference deletion at a receiving end to carry out multi-user detection; 2) the symbol-level NOMA is realized by using technologies such as sparse/dense expansion, sequence design and the like, and multi-user detection can be realized at a receiving end by adopting technologies such as message transmission, serial interference deletion and the like.
Most of the researches of the two types of NOMA are carried out under the assumption of synchronous transmission, which not only requires accurate synchronization among users, but also greatly influences the transmission efficiency of data. And the non-synchronous transmission can avoid strict synchronization among users, and can overcome the problems to a certain extent. At present, compared with the NOMA of bit level, the research of multi-user detection of NOMA of non-synchronous symbol level is not related, and needs to be studied deeply. LDS is used as a symbol-level NOMA, and a pre-designed codebook is utilized to map bit information of each user to a plurality of frequency resources in a sparse manner to realize overload, so that the spectrum efficiency is improved, and the system access quantity and the throughput are improved. In asynchronous transmission, data superimposed on the same frequency resource by each user in the LDS system are staggered in time, and a multi-user detection receiver under the assumption of synchronization cannot achieve correct reception.
Disclosure of Invention
In order to solve the multi-user detection problem of the symbol-level NOMA of the uplink LDS system in the asynchronous transmission scene, the invention discloses a symbol-level NOMA asynchronous receiving method based on a cross-slot message transfer algorithm, which aims to solve the technical problems that: the code element of each user is estimated by spanning the time slot on each frequency resource for transmission by using a message transmission method, so that the interference among multiple users caused by non-synchronization is eliminated, the multi-user detection of the LDS system under the non-synchronization is realized, and the transmission efficiency of the system is improved.
The purpose of the invention is realized by the following technical scheme.
A symbol-level NOMA non-synchronous receiving method based on a cross-slot message transfer algorithm comprises the following steps:
the method comprises the following steps that firstly, a transmitting end carries out channel coding, modulation, LDS codebook mapping and shaping filtering on respective information bits of K users in sequence to obtain a waveform signal to be transmitted, and all the users adopt the waveform signal which is known by a receiver and is the same.
The sending end has K users to carry out LDS uplink transmission. Sequentially coding and Mod-order modulating the information bits of any user k to generate a modulation signal b with the length pk。
Mapping each Mod modulation symbol to an N-dimensional LDS complex codebook with the size of K to generate a complex LDS codeword ck. The code book has the real part and the imaginary part of each code element with mapping relation of 2ModPossible values are selected and positive and negative pairs appear.
Obtained by shaping filtering:
wherein,the i-th, i-1 … p symbols of user K, K-1 … K on frequency resource N, N-1 … N, and s (T) is a waveform signal with unit energy of a period T. And all users canA waveform signal known and identical to the receiver is used.
And step two, the waveform signal generated by the transmitting end in the step one passes through a Rayleigh fading channel in an asynchronous mode, and the receiving end receives the waveform signal on each frequency resource respectively.
Considering the channel type as Rayleigh fading hkCN (0,1), K1 … K, and the channel coefficients are known to the receiverAnd default frame synchronization has been achieved, considering only the case of symbol asynchronous transmission. Thus, with τkDenotes the transmission delay of user k, and 0 ═ τ1≤…≤τk< T. N (t) is a bilateral power spectral density of N0White Gaussian noise of/2. Receiving a signal y of a signal on a frequency resource nn(t) is expressed as:
wherein h isk,nRepresenting the channel coefficient h of user kkValue n on the nth frequency resourcen(t) denotes the truncation of n (t) on frequency resource n.
And step three, performing matched filtering and down sampling on the signals on the frequency resources output in the step two to obtain the symbol sequences received on the frequency resources.
Signal y on each frequency resourcen(T), N-1 … N is mapped to waveform s (T- (i-1) T- τk) And K is in the direction of 1 … K, namely, the two directions are convoluted and downsampled to obtain signals matched and filtered on each frequency resource by each user
Wherein,represents interference of other users to user k, and isThe interference of (2) is caused by the time slot and the adjacent time slot,for the sum of the interference of the other users to user k and white Gaussian noise, hk,nRepresenting the channel coefficients of user k on frequency resource n,and | hm,nL respectively represent the complex conjugate and the modulus of the channel coefficient of user m ≠ k on frequency resource n,to representCorresponding white gaussian noise.
And step four, estimating the code element of each user by spanning the time slot on each frequency resource for the symbol sequence output by the step three by using a message transmission method so as to eliminate the interference among multiple users brought by non-synchronization.
Symbol sequence output by step threeIs composed ofAnd the rest of the users are superposed with the adjacent time slot symbols in the time slot, so that the factor graph utilized by the message transfer algorithm comprises a time dimension, and the algorithm is called a cross-time-slot message transfer algorithm in the following. In the factor graph, the transmitted symbolsAs a node of the user,as a sum node. And as is known from the formula (1),and andthere are "edges" in between.
The detection process of the cross-slot message passing algorithm is divided into two rounds. First round detection as estimationThe positive and negative characteristics of the composition; the second round being detected by the first roundBased on the positive and negative characteristics ofMagnitude of absolute value. After the two-wheel detection is finished, summarizing all frequency resourcesIs calculated to obtainAn estimate of (d).
Considering LDS as a complex codebook, the detection of which by the receiving end will be divided into a real part and an imaginary part. According to the theorem of central limit,real part ofAnd imaginary partAre respectively expressed as a conditional probability density function:
wherein,r (-) and I (-) denote the real and imaginary parts of the complex variable, respectively,andrespectively representThe real and imaginary parts, E, of the symbols possibly being selected on the codebookR[·]And EI[·]Means, V, representing the real and imaginary parts of a complex random variableR[·]And VI[·]The variances of the real and imaginary parts of the complex random variable are represented, respectively. Considering that the size of the code element in the LDS codebook is symmetrical about the origin, the first round of detection is selectedIn the second round of the test,is ci k,nOne group of the selectable symbols and the first round of detectionAnd the real part of the code element with consistent positive and negative.Is thatOne group of the selectable symbols and the first round of detectionAnd symbol imaginary parts with consistent positive and negative polarities.
From the equations (3.1) and (3.2),the log-likelihood ratios of the real and imaginary parts are expressed as
Is a message transmitted by the node to the user node. Wherein the first round of detection takes R (x)1)=I(x1)=+1,R(x2)=I(x2) -1; in the second round of detection, takeWhereinIs thatThe real part of the optional code element in the codebook is obtained by the first detectionComparison of positive and negative with the same absolute valueA large value; whileIs also thatThe real part of the optional symbol in the codebook, but is not equal toDifferent from the first round of detectionThe absolute value of the positive and negative is small. Similarly, takeWhereinIs thatThe imaginary part of the optional code element in the code book is obtained by satisfying the first detectionA value having a large absolute value of positive and negative; whileIs also thatImaginary part of optional symbol in codebook, but notDifferent and satisfy the first round of detectionThe absolute value of the positive and negative is small.
User node andthe messages transmitted by the nodes being user nodesReceived (a)Andand only the message needs to be forwarded to each of its edges.
After the two-wheel detection is finished, the detection is combined with the first wheel detectionAndpositive and negative characteristics of and obtained by the second round of detectionAndthe magnitude of the absolute value, get pairAn estimate of the exact likelihood.
Subsequently exporting on each resourceBy the probability of occurrence of each codewordAnd the output result of the step four is used for next decoding of the mapping.
And step five, utilizing the probability of each code word of the user output in the step four and combining the LDS codebook mapping relation to solve the LDS codebook mapping to obtain an estimated value of the modulation signal.
According to the step four outputOf each code wordCombining the mapping relation of LDS codebook of each user to obtain modulation symbol
And step six, demodulating and de-channel coding the modulation symbols obtained in the step five in sequence to obtain an estimated value of information bits, and completing the multi-user detection of the asynchronous uplink LDS system.
For step five modulation symbolsDemodulating and decoding the channel to obtain the estimated value of the information bitNamely, multi-user detection of the LDS system under non-synchronization is realized.
Has the advantages that:
the invention discloses a symbol-level NOMA asynchronous receiving method based on a cross-time-slot message transfer algorithm, which introduces time dimension into a traditional two-dimensional factor graph to form the cross-time-slot message transfer method based on a three-dimensional factor graph model, estimates a code element of each user by utilizing the message transfer method to cross time slots on each frequency resource used for transmission, realizes multi-user detection of an asynchronous LDS system, solves the problem that the traditional symbol-level NOMA system can only synchronously transmit, realizes symbol-level NOMA asynchronous receiving, improves data transmission efficiency, expands the capacity range of the LDS system, and enhances the availability of the LDS in massive Internet of things communication.
Drawings
FIG. 1 is a diagram of a transmitter system model for an unsynchronized LDS system;
FIG. 2 is a diagram of an interference model for an LDS transmission system with symbol asynchronism;
FIG. 3 is a system model of an unsynchronized multi-user receiver;
FIG. 4 is a factor graph model of a cross-slot messaging algorithm;
fig. 5 is a flow chart of a symbol-level NOMA asynchronous receiving method based on a cross-slot message transfer algorithm disclosed by the invention.
Detailed description of the invention
In order to make those skilled in the art understand the implementation idea of the present invention more deeply, the technical solution in the embodiment of the present invention will be described carefully and clearly with reference to the drawings in the embodiment of the present invention. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without any creative efforts shall fall within the protection scope of the present invention.
The following describes specific steps of the embodiment of the present invention with reference to specific scenarios:
the symbol-level NOMA asynchronous receiving method based on the cross-slot message transfer algorithm disclosed by the embodiment specifically comprises the following implementation steps:
the method comprises the following steps that firstly, a transmitting end carries out channel coding, modulation, LDS codebook mapping and shaping filtering on respective information bits of K users in sequence to obtain a waveform signal to be transmitted, and all the users adopt the waveform signal which is known by a receiver and is the same.
As shown in fig. 1, the LDS uplink transmission is performed asynchronously by K ═ 6 users. Information bits of an arbitrary user k are sequentially encoded and Mod-2-order QPSK modulated, and a modulated signal having a length p is generated:
where the subscript k represents user k.
Every Mod 2 modulation symbols are mapped to N4-dimensional LDS complex codebook with size K6 [ [ (c)1)T,…,(cK)T]TGenerating a complex LDS code word:
ck=[ck,1,...,ck,N]T
wherein [. ]]TRepresenting the transpose of a matrix or vector, N can be considered as a spreading factor. The code book has the real part and the imaginary part of each code element with mapping relation of 2ModPossible values are obtained, and the optional code elements are symmetrical about the origin and appear in pairs of positive and negative.
And (3) performing forming filtering by using a root raised cosine s (t) sampled for 7 times in a period to obtain:
wherein,representing a userOn spread spectrum resourcesThe i-th symbol above is 1 … p symbols, s (T) has a period T and has unit energy, and the receiver knows the waveform information of s (T).
And step two, the waveform signal generated by the transmitting end in the step one passes through a Rayleigh fading channel in an asynchronous mode, and the receiving end receives the waveform signal on each frequency resource respectively.
Considering the channel type as Rayleigh fading hkCN (0,1), K1 … K, and the channel coefficients are known to the receiverAnd default frame synchronization has been achieved, considering only the case of symbol asynchronous transmission. Thus, with τkDenotes the transmission delay of user k, and 0 ═ τ1≤…≤τk< T. N (t) is a bilateral power spectral density of N0White Gaussian noise of/2. Receiving a signalSignal y on frequency resource nn(t) is expressed as:
wherein h isk,nRepresenting the channel coefficient h of user kkValue n on the nth frequency resourcen(t) denotes the truncation of n (t) on frequency resource n.
And step three, performing matched filtering and down sampling on the signals on the frequency resources output in the step two to obtain the symbol sequences received on the frequency resources.
Signal y on each frequency resourcen(T), n-1 … 4 is mapped to waveform s (T- (i-1) T- τk) And k is in the direction of 1 … 6, i.e. the two directions are convoluted and down-sampled to obtain signals matched and filtered by each user on each frequency resource
Wherein, among others,represents interference of other users to user k, and isThe interference of (2) is caused by the time slot and the adjacent time slot,for the sum of the interference of the other users to user k and white Gaussian noise, hk,nRepresenting the channel coefficients of user k on frequency resource n,and | hm,nI respectively indicates that the user m is not equal to k in frequencyThe complex conjugate and the modulus of the channel coefficients on resource n,to representCorresponding white gaussian noise. ,representing the autocorrelation coefficients.
And step four, estimating the code element of each user by spanning the time slot on each frequency resource for the symbol sequence output by the step three by using a message transmission method so as to eliminate the interference among multiple users brought by non-synchronization.
Considering the symbol asynchrony between users, as shown in fig. 2, the output after matched filtering and down sampling is the superposition of the symbol sequence and the symbols of the other users in the current time slot and the adjacent time slot. Therefore, we introduce the time dimension into the traditional two-dimensional factor graph to characterize the message passing process, and form the cross-slot message passing algorithm on the basis of the time dimension. The symbols transmitted in the factor graph are shown in FIG. 3As a node of the user,as a sum node. As can be seen from the equation (5),is that Andthus, a nodeThe user nodes are connected by 'edges', and the rest nodes are similar.
The detection process of the cross-slot message passing algorithm is divided into two rounds. Each round of detection will be performed niI is 1,2 iterations. First round detection as estimationPositive and negative characteristics of (1), output characterization after iteration is overMaximum likelihood ratio of positive and negative characteristics for next detection; the second round being detected by the first roundBased on the positive and negative characteristics ofMagnitude of absolute value, end of iteration outputAnd (4) accurate detection results. To obtain finallyThe probability of occurrence of the codeword is obtained. In each round of detection, the message is repeatedly iterated on the 'edge' of the factor graph, each iteration and the node and the user node are processed once until the maximum iteration times is reached, and an estimation result is output.
Considering LDS as a complex codebook, the detection of which by the receiving end will be divided into a real part and an imaginary part. According to the central limit theorem, in equation (6)Can be approximated as a gaussian variable, thenReal part ofAnd imaginary partAre respectively expressed as a conditional probability density function: :
wherein,r (-) and I (-) denote the real and imaginary parts of the complex variable, respectively,andrespectively representThe real and imaginary parts, E, of the symbols possibly being selected on the codebookR[·]And EI[·]Means, V, representing the real and imaginary parts of a complex random variableR[·]And VI[·]The variances of the real and imaginary parts of the complex random variable are represented, respectively. Considering that the symbol size in the LDS codebook is symmetric about the origin, for simplicity, the first round of detection is selectedIn the second round of the test,is thatOne group of the selectable symbols and the first round of detectionAnd the real part of the code element with consistent positive and negative.Is thatOne group of the selectable symbols and the first round of detectionAnd symbol imaginary parts with consistent positive and negative polarities.
From the equations (7.1) and (7.2),the log-likelihood ratios of the real and imaginary parts are expressed as
Is a message transmitted by the node to the user node. Wherein the first round of detection takes R (x)1)=I(x1)=+1,R(x2)=I(x2) -1; in the second round of detection, takeWhereinIs thatIn a codebookThe real part of the optional code element and obtained by the first detectionThe absolute value is larger with the same positive and negative; whileIs also thatThe real part of the optional symbol in the codebook, but is not equal toDifferent from the first round of detectionThe absolute value of the positive and negative is small. Similarly, takeWhereinIs thatThe imaginary part of the optional code element in the code book is obtained by satisfying the first detectionA value having a large absolute value of positive and negative; whileIs also thatImaginary part of optional symbol in codebook, but notDifferent and satisfy the first round of detectionThe absolute value of the positive and negative is small. In addition, the first and second substrates are,andcalculated using the following formula:
wherein, andto representThe mean and the variance of the imaginary part, andthe mean and variance of (c) may be calculated based on messages input by the user node, as follows:
wherein R (x)1),R(x2),I(x1),I(x2) The meaning is the same as that expressed by the formula (8). Notably, due to the first iteration R (x)1)=I(x1)=+1,R(x2)=I(x2) Equation (11) is reduced to-1, the following equation:
The message transmitted by the user node to the sum node is the user nodeReceived (a)Andand only this message needs to be forwarded to each of its edges for the next round of processing by the sum node.
After the two-wheel detection is finished, the first wheel is detectedAndare respectively characterizedAndmaximum likelihood function of positive and negative characteristics, and second detectionAndare respectively characterizedAndmaximum likelihood function of absolute value magnitude.
The first round of detection isAndaccording to the basic formula of the maximum likelihood function shown in formula (8), the following is calculated:
wherein,andrespectively representThe probability of being a positive number and a negative number,andrespectively representThe probability of a positive number and a negative number.
The second round of detection isAndto obtainProbability of larger and smaller absolute valuesAndsee formula (13.1).Andthe algorithm is the same, see equation (13.2).
At this time, the process of the present invention,andthe probability of possible values of (a) can be expressed as:
wherein, the formulas (15.1) and (15.2) respectively representIn the case of positive and negative values, the equations (16.1) and (16.2) represent the values, respectivelyBoth positive and negative.
Will be provided withAndmultiply by each other and getNormalizing a group of results corresponding to possible values in the corresponding codebook to obtain a normalized resultProbability of possible valuesTo representSoft information of the estimated value of (a).
is composed ofThe corresponding serial numbers are multiplied.Characterization pairThe estimation result of (2).
And step five, utilizing the probability of each code word of the user output in the step four and combining the LDS codebook mapping relation to solve the LDS codebook mapping to obtain an estimated value of the modulation signal.
According to the code word c output by the step four for each userkIs estimated byFirstly, the LDS codebook is demapped, andas a pair with a set of LDS code words corresponding to the maximum value ofIs estimated value ofByThe estimated value of the modulation symbol of the user k can be obtained
And step six, demodulating and de-channel coding the modulation symbols obtained in the step five in sequence to obtain an estimated value of information bits, and completing the multi-user detection of the asynchronous uplink LDS system.
For step five modulation symbolsDemodulating and decoding the channel to obtain the estimated value of the information bitNamely, multi-user detection of the LDS system under non-synchronization is realized.
The above detailed description is intended to illustrate the object and technical solution of the present invention, and it should be understood that the above detailed description is only an example of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (1)
1. A symbol-level NOMA non-synchronous receiving method based on a cross-time slot message transfer algorithm is characterized in that: comprises the following steps of (a) carrying out,
the method comprises the following steps that firstly, a transmitting end carries out channel coding, modulation, LDS codebook mapping and forming filtering on respective information bits of K users in sequence to obtain waveform signals to be transmitted, wherein all the waveform signals are the same and known by a receiver;
step two, the waveform signal generated by the transmitting end in the step one passes through a Rayleigh fading channel in an asynchronous mode, and the receiving end receives the waveform signal on each frequency resource respectively;
step three, performing matched filtering and down-sampling on the signals on the frequency resources output in the step two to obtain symbol sequences received on the frequency resources;
step four, estimating the symbol sequence output in the step three by spanning the time slot on each frequency resource by using a message transmission method so as to eliminate the interference among multiple users brought by non-synchronization;
step five, utilizing the probability of each code word of the user output in the step four and combining the LDS codebook mapping relation to solve the LDS codebook mapping to obtain an estimated value of the modulation signal;
step six, demodulating and de-channel coding the modulation symbols obtained in the step five in sequence to obtain an estimated value of information bits, and completing the multi-user detection of the asynchronous uplink LDS system;
the first implementation method comprises the following steps of,
a sending end has K users to carry out LDS uplink transmission; sequentially coding and Mod-order modulating the information bits of any user k to generate a modulation signal b with the length pk;
Mapping each Mod modulation symbol to an N-dimensional LDS complex codebook with the size of K to generate a complex LDS codeword ck(ii) a The code book has the real part and the imaginary part of each code element with mapping relation of 2ModPossible values are selected, and positive and negative pairs appear;
obtained by shaping filtering:
wherein,a waveform signal representing the i-th, i-1 … p symbols of user K, K-1 … K on frequency resource N, N-1 … N, and s (T) representing unit energy with a period T; all waveform signals are identical and known to the receiver;
the second step is realized by the method that,
considering the channel type as Rayleigh fading hkCN (0,1), K1 … K, and the channel coefficients are known to the receiverAnd default frame synchronization has been achieved, considering only the case of symbol asynchronous transmission; thus, with τkDenotes the transmission delay of user k, and 0 ═ τ1≤…≤τk< T; n (t) is a bilateral power spectral density of N0White Gaussian noise of/2; receiving a signal y of a signal on a frequency resource nn(t) is expressed as:
wherein h isk,nRepresenting the channel coefficient h of user kkValue n on the nth frequency resourcen(t) denotes the truncation of n (t) on frequency resource n;
the third step is to realize the method as follows,
signal y on each frequency resourcen(T), N-1 … N is mapped to waveform s (T- (i-1) T- τk) K is 1 … K direction, i.e. the two directions are convoluted and down-sampled to obtain the matching of each user on each frequency resourceMatched filtered signals
Wherein,represents interference of other users to user k, and isThe interference of (2) is caused by the time slot and the adjacent time slot,for the sum of the interference of the other users to user k and white Gaussian noise, hk,nRepresenting the channel coefficients of user k on frequency resource n,and | hm,nL respectively represent the complex conjugate and the modulus of the channel coefficient of user m ≠ k on frequency resource n,to representCorresponding white gaussian noise;
the implementation method of the fourth step is that,
symbol sequence output by step threeIs composed ofAnd the superposition of other users on the code elements of the time slot and the adjacent time slot, so that the factor graph utilized by the message transmission algorithm contains a time dimension, and the algorithm is called a cross-time-slot message transmission algorithm in the following; in the factor graph, the transmitted symbolsAs a node of the user,as a sum node; and as is known from the formula (1),and andthere is an "edge" between;
the detection process of the cross-time slot message transmission algorithm is divided into two rounds; first round detection as estimationThe positive and negative characteristics of the composition; the second round being detected by the first roundBased on the positive and negative characteristics ofThe magnitude of the absolute value; after the two-wheel detection is finished, summarizing all frequency resourcesIs calculated to obtainAn estimated value of (d);
the LDS is considered as a complex codebook, and the detection of the LDS by a receiving end is divided into a real part and an imaginary part; according to the theorem of central limit,real part ofAnd imaginary partAre respectively expressed as a conditional probability density function:
wherein,r (-) and I (-) denote the real and imaginary parts of the complex variable, respectively,andrespectively representThe real and imaginary parts, E, of the symbols possibly being selected on the codebookR[·]And EI[·]Representing complex randomMean of real and imaginary parts of variables, VR[·]And VI[·]Respectively representing the variances of the real part and the imaginary part of the complex random variable; considering that the size of the code element in the LDS codebook is symmetrical about the origin, the first round of detection is selectedIn the second round of the test,is thatOne group of the selectable symbols and the first round of detectionA code element real part with consistent positive and negative characters;is thatOne group of the selectable symbols and the first round of detectionA symbol imaginary part with consistent positive and negative;
from the equations (3.1) and (3.2),the log-likelihood ratios of the real and imaginary parts are expressed as
Is a message transmitted by the node to the user node; wherein the first round of detection takes R (x)1)=I(x1)=+1,R(x2)=I(x2) -1; in the second round of detection, takeWhereinIs thatThe real part of the optional code element in the codebook is obtained by the first detectionThe absolute value is larger with the same positive and negative; whileIs also thatThe real part of the optional symbol in the codebook, but is not equal toDifferent from the first round of detectionA smaller absolute value of positive and negative; similarly, takeWhereinIs thatThe imaginary part of the optional code element in the code book is obtained by satisfying the first detectionA value having a large absolute value of positive and negative; whileIs also thatImaginary part of optional symbol in codebook, but notDifferent and satisfy the first round of detectionA smaller absolute value of positive and negative;
the message transmitted by the user node to the sum node is the user nodeReceived (a)Andand only the message needs to be forwarded to each of its edges;
after the two-wheel detection is finished, the detection is combined with the first wheel detectionAndpositive and negative characteristics and second round of inspectionMeasured to obtainAndthe magnitude of the absolute value, get pairAn estimate of the exact likelihood;
subsequently exporting on each resourceBy the probability of occurrence of each codewordThe output result of the step four is used for next decoding of the mapping;
the fifth step is to realize that the method is that,
according to the occurrence probability of each code word output in the step fourCombining the mapping relation of LDS codebook of each user to obtain modulation symbol
The sixth realization method comprises the following steps of,
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